The same short rounded cap is worn by Muslim men across the world under a long list of local names. Taqiyah is the general Arabic term. In West Africa and among African American Muslims it is the kufi. In South Asia it is the topi, and the openwork crocheted white cap of Bengali and north Indian usage is a distinct and recognisable form of it. In Indonesia and Malaysia the songkok or peci is a stiff brimless cap, usually black velvet, of a quite different cut. Central Asia has the square embroidered doppa and the araqchin.
Its commonest function is as a base. A turban is wound over a cap rather than directly onto the head, so a taqiyah is worn under the imamah in traditions that use one, and under the larger headcloths of the Gulf under the agal. Worn alone it is simply a cap.
There is no single religious specification for its colour, material or shape, which is why the regional forms vary so freely. White is common for prayer and for pilgrimage; embroidery, colour and pattern are matters of local dress. The cap is also, in several countries, a marker of something other than piety alone: the peci became a national symbol in Indonesia, worn by presidents of every religion at state occasions, which is not a religious use of it at all.